Geological models, such as petroleum reservoir geological models, are often utilized by computer systems for simulation. For example, computer systems may utilize petroleum reservoir geologic models to simulate the flow and location of hydrocarbons within a reservoir. Geological models are typically formed utilizing thousands or millions of geologic cells, with each cell corresponding to a location and a physical geologic or petrophysical property. The number of cells or cell size in a model is generally determined by the computing capabilities of geomodeling packages or flow simulator and the level of heterogeneity geomodelers want to capture.
Accurate reservoir performance forecasting requires three-dimensional representation of the geological model. The geological model is commonly built with the use of well and seismic data and stochastic simulation techniques. Simulated rock property values are filled in the three-dimensional cells constructed at a given scale. Cell dimensions are changed according to the needs of flow simulation. The cells can be “upscaled” into larger (“coarser”) cells, “downscaled” into smaller (“finer”) cells or a combination thereof.
Conventional downscaling methods typically resample the property values from coarse grids to fine grids, which gives the same property value of all fine-grid cells located in the same coarse grid. Sharp changes can be commonly created across the coarse grid boundaries. For example, when a coarse grid model with four cells is downscaled into a sixteen cell unit, the downscaled model still keeps the same values as the coarse model. The simple conventional approach can certainly maintain the data value consistency between the initial model and the downscaled model; however, the conventional downscaled model falls short in numerous regards, including: inability to capture the fine-scale heterogeneities, inability to preserve the continuity across the coarse grid areas, inability to quantify static property uncertainty and inability to condition to available fine-scale hard data.
Kriging with local varying mean (LVM) provides a channel for adding coarse-scale data into the kriging system hence into spatial estimators. This type technique is, for example, described in the following document:
Goovaerts, P., 1997, “Geostatistics for Natural Resources Evaluation”, Oxford University Press, New York, p. 496.
However, the coarse information is used only as an expected value replacing the local simple kriging (SK) stationary mean. Kriging with LVM can not reproduce the local mean, and hence cannot reproduce the coarse data value exactly.
The goal of block kriging is to estimate block values through weighted linear combinations of conditioning point data with the weights obtained by solving a block kriging system. Block kriging is similar to an upscaling process, as opposed to the inverse process of downscaling. This technique is, for example, described in the following documents:
Journel, A. and Huijbregts, C. J.: 1978, Mining Geostatistics, Academic Press, New York.
Isaaks, E. and Srivastava, R.: 1989, An introduction to applied geostatistics, Oxford University Press, New York.
A block sequential simulation (bssim) algorithm is currently utilized for integrating coarse-scale block average data of any shape (e.g., remove sensing or seismic travel-time tomographic data) with fine data. This technique is, for example, described in the following documents:
Liu, Y., 2007, “Geostatistical integration of linear coarse-scale data and fine-scale data”, PHD dissertation, Stanford University, California, p. 211.
Liu, Y. and Journel, A. G., 2009, “A package for geostatistical integration of coarse and fine scale data”, Computers & Geosciences, 35(3), 527-547.
Unfortunately, available computing power and time constraints limit the number of cells that may be practically utilized by geologic models. Thus, bssim is limited to downscaling small models that have less than 1000 coarse grid cells due to its excessive memory costs.
Therefore, a need exists for a practical downscaling algorithm for geological modeling to capture the fine-scale heterogeneities, to preserve the continuity across the coarse grid areas, to quantify static property uncertainty, and to condition to available coarse and fine-scale hard data, all while using the least amount of memory.